Analysis for Fashion Emergence by Agent-based Simulation
Fujii ShintaroWang ZhongtuoXia Haoxiang
Institute of Systems Engineering, Dalian University of Technology
116024 Dalian China
ABSTRACT
In this paper, how fashion emerges is studied. Fashion is aprocess of social diffusion by which a new style is adopted by consumers interacting with each other.
The basic process of fashion emergences is as follow. At first, a new phenomenon is adopted by a few people. When it comes to majority through the interaction among individuals, it becomes a fashion.
This paper proposes two models. Both models are based on the threshold to determine whether agents adopt fashion or not. The first model is an "everyone knows everything" model, which analyzeglobal information. The other is "each one knows only their own neighbors" which can explain the individuals' interaction causing fashion (local information). Last, to understand how fashion emerges, both models are integrated.
Key wordsEmergence, Modeling, Interaction, Agent-based Simulation, Cellular Autmata
- INTRODUCTION
The fashion system consists of all those people and organizations involved in creating symbolic meanings and transferring these meanings to cultural goods. Fashion is not only peculiar to clothes. It includes a prevailing or preferred manner of dress, adornment, behavior, or way of life at a given time[1]. It can be said that fashion is a process of social diffusion by which a new style is adopted by some group(s) of consumers interacting with each other[1][2]. It should be noticed two points about fashion emergence; one is that fashion is the process to expand from minority to majority, and another is that it comes of the interaction among members. Especially the former point seems reverse to Dynamic Social Impact Theory (DSIT) sayingthe majority expands further and the minority reduces in number but not disappears with time[3].
As stated by Minami, fashion emerges when “a certain number of people are psychologically brought to adopt same collective behavior that begins on an intention during a certain period[4]”. The trickle-down theory has explained fashion as following[5]:as subordinate groups are brought to adopt the status symbols of the groups above them, dominant styles of the upper class trickle-down to those below. In addition to this force, Saito observed the reverse force[6]. Fashion consisted of both forces, trickle-down and –up[7], but this task is not so easy in modern times. It is often more accurate to speak of a trickle-across effect, where fashion diffuse horizontally among members of the same social group[8]. Because people tends to compare themselves to and mimic others who are similar[1].
Simmel explains the psychological factor to accept fashion by two desires[9]. It consists of “the desire to distinguish oneself from the others” and “the desire to conform to a society, a group or to align with others”. E. M. Rogers categorizes the fashion adopters into five stages from innovators to laggards according to their adopting speed[10]. The stronger desire to be distinguished from others customers have, the earlier they adopt fashion. A new phenomenon is adopted first by innovators who are eager to change. And people come to like things simply as a result of seeing more often. The principle of social proof explains the psychology of those who adopt later from the influence from others[11]. It states “The actions of those around us will be important in defining the answer”. It is a form of collective behavior, or a wave of social conformity. It can be said the relationship with others creates and spreads fashion.
As mentioned above, the fashion emerging process is as follows: a few people who have the desire to distinguish from others create a new phenomenon. Some people follow them and as adopters increase, the presence of large number of people in a consumer environment increases arousal levels, so consumer’s subjective experience of a setting tends to be more intense, so those who desire to conform are brought to imitate the behavior[2].
However, it is hard to determine how fashion emerges actually because we can never recognize fashion before a phenomenon becomes fashion. Therefore it is impossible to follow quantitative data of fashion back to its appearance. This paper tries to explore how the interactions create fashion by applying agent-based simulation. The interactionsare considered as local interaction, for instance, oral communications among individuals, and global interaction between the whole environment where they live and each individual.This paper introduces two interaction models. First, the global interaction is analyzed, then the local interaction is built, last the integrated model is proposed.
- GLOBAL INTERACTION MODEL
The number of people adopt a phenomenon makes him or her conform is called as threshold. It is peculiar to each person. The lower threshold is, the stronger the desire to distinguish from others is. People are considered to behave based on their own threshold. If the number of people adopt a phenomenon exceeds his or her threshold, he or she adopts it. As adopters increase, those who has higher threshold come to adopt it. One attribute of fashion is the positive feedback which adopters create further more adopters.
We compose the behavior of agent as following:
Each agent is influenced by others.
Each agent behaves according to received influence.
Each agent has peculiar threshold for influence
The first proposed model is global interaction model. Box bar in Graph.1 shows the example that the distribution of threshold and line is accumulation ratio of threshold. For example, 5 percent people have the threshold which responses under 10 percent. If 10 percent people including those have high threshold initially happen to adopt a phenomenon, some whose threshold is more than 10 percent stop adopting and others have less than it adopt newly, there are 5 percent people adopt it at the next step. Then somebody whose threshold is less than 5 percent keep their attitudes, and at last, no one adopts it. If initial adopters are 30 percent, other 12 percent people have under 20 percent threshold and 21 percent who have under 30 percent threshold are added, so totally 38 percent people adopt it, and at the next step, people have threshold under 38 percent response them.
In this case, if a phenomenon begins initial adopters under point P, a phenomenon reduces the number step-by-step, eventually is disappeared. On the other hand, if initial adopters are more than point P, it expands to all members at last.
Graph.1the expansion and reduction of phenomenon
This model demonstrates that expansion or reduction of phenomenon depends on the threshold distribution and the number of initial adopters. This is “everyone knows everything” model because all agents know same information at the same time. This information means here “how many people adopt a phenomenon”. People behave based on their own threshold and same information, and interact with the environment where they live. We define this model as “global interaction” based on global information.
- CONCEPT OF AGENT-BASED MODEL
Everyone influences to all others in the previous global interaction model. However, it is impossible to recognize whole environment because of our infinite perception. Next model takes consider a range of perception. This model is regarded as a kind of Cellular Automata (CA). The feature of CA is as following:
Discrete Space: It consists of not continuous but discrete cells.
Discrete time: the value of each cell is updated at some discrete interval.
Discrete state: Each cell has one of the finite values.
Uniformity: Each cell is homogenous, and is put in order regularly.
Simultaneous updating: All cells are updated simultaneously.
Spatial local rule: Only nearby cells influence the cell updating.
Temporal local rule: Only the last few steps (usually the exactly previous step) influence the cell updating.
Universal function: Each cell applies the common value and the function as the updating rule.
This is “each agent knows only the neighbors” model. This model investigates how the behavior of “individuals” with local information influences the whole system.
The model consists of 100 agents; everyone has the possibility to adopt a phenomenon. They live in a discrete space with 10 * 10 cells. Each agent is located on each cell without overlapping. One cell represents one agent here. This space stands for not physical but mental space, and any movements of agents are not considered. Each agent has the attitude and the tendency; the attitude can change but the tendency is fixed to each one. The attitude is adopting a phenomenon or not. If an agent is an adopter, it has an influence on its neighbors. The total amount of influence by neighbors adopting a phenomenon decides the attitude, and it also affects others again. We define this as “the local interaction” based on “the local information”. This paper applies Neumann neighborhood, which means that each agent checks four directions neighbors (up, down, left, and right) with the exception that marginal agents do two or three. The important thing is that even if adopters are majority in the environment, they are minority for an agent if the agent has only an adopter in neighbors. When adenotes an attitude: adopting is 1, not adopting is 0, and i, j shows agent’s position, the influence LI (i, j)from neighbors is as following:
LI (i, j)= a (i+1, j) + a (i-1, j) + a (i, j+1) + a (i, j-1)
( 0 ≦LI ≦4) (1)
The tendency of agents is classified into two, i.e. pioneers and followers. Pioneers have a stronger desire to distinguish themselves from others so their adopting speed is early. And the other desire, i.e. “the desire to conform to society”, is stronger for the followers, i.e., they adopt the phenomenon later. In short, pioneers hope to be minority while followers follow majority in the group. In this paper, their adopting rule is as following (Table. 1).
Pioneers: When given influence is one, then they adopt it. If zero or more than three, they don’t. In case there are just two adopters around them, their attitude is kept.
Followers: When there are more than three adopters, they follow. If two neighbors adopt phenomenon, they preserve their own attitude. In other case, adopter is less than one, they won’t adopt.
Influence / 0 / 1 / 2 / 3 / 4Pioneer / ☓ / ○ / △ / ☓ / ☓
Follower / ☓ / ☓ / △ / ○ / ○
○:adopt, ☓: not adopt, △: keep current attitude
Table. 1 Adopting rule
The attitude of each agent at the next step is based on their own tendency and the current attitudes of their neighbors. When T(i, j) denotes the tendency, t means current step, the next attitude at+1(i, j) is given by the following function F using LI from (1):
at+1(i, j) = F(LIt (i, j) ,Tt (i, j) )(2)
Then the adopting rules of pioneers and followers are as following:
Pioneer:
at+1(i, j) = {LI | if It (i, j)=1, 0 | if LIt (i, j)=0 || LIt (i, j) >2}(3)
Follower:
at+1(i, j) = {1 | if LIt (i, j) > 2, 0 | if LIt (i, j) <2 }(4)
If LIt (i, j)=2, then at+1(i, j) will not change in the both tendencies.
The difference between CA and this model is that this model doesn’t apply the uniformity and the universal function. The difference of the adopting rule of each cell is the feature of this model.
Putting pioneers, followers and initial adopters on a space at random, the simulation is then run 30 steps in circling. The average of adopters in the last 5 steps in this 30 stepping is applied as a final adopters in this run. Repeating it enough times under the same condition, the same number of pioneers, followers and initial adopters but allocation differs from each time, provides the maximum number of final adopters and the average of final adopters on the condition.
- LOCAL INTERACTION MODEL
Graph.2a, b and c show the average number of final adopters and the relation between initial adopters and pioneers. The number of final adopters becomes larger as the number of initial adopters increases on the condition of the same number of pioneers (Graph.2a). And when fixing the number of initial adopters and change the number of pioneers, if initial adopters are a few, final adopters expand as increasing pioneers. However if pioneers are many, final adopters decrease as increasing pioneers.
Graph.2b is the expanding rate of the number of final adopters to the number of initial adopters. The more initial adopters are, the more pioneers are needed for expanding. It becomes larger as pioneers increase in the case with fewer initial adopters and it decreases accordingly in the case with more initial adopters. This means initial adopters expand more than at the first step when pioneers are many and initial adopters are a few or when pioneers are a few and initial adopters are many but too many initial adopters have opposite effect. In the condition with fewer initial adopters, the more pioneers are, the more final adopters are at the same number of initial adopters. On the contrary condition of more initial adopters, final adopters decrease as pioneers increase but they converge to around 60 final adopters in spite of the number of initial adopters.
Final adopters are always lass than initial adopters between 13 and 36 pioneers. If there are more than 36 pioneers, initial adopters expand when they are minority and if pioneers are less than 13, initial adopters expand when they are majority but too many initial adopters decrease the number of final adopters. The number of pioneers determines the capacity of final adopters and whether a phenomenon expands or reduces.
Consider the case fixing the number of pioneers to 0; consists of only followers. Expanding rate exceeds 1.0 when there are more than 61 initial adopters. In this case, majority of adopting a phenomenon expands more. This result may explain the consolidationLatane insists this in his DSIT[3].
Graph.2athe relation between the number of initial adopters and pioneers
Graph.2bThe ratio of final adopters to initial adopters
Graph.2c shows that the maximum, minimum and average number of final adopters as increasing the number of the initial adopters fixing the number of the pioneers to 70.
Graph.2cThe number of final adopters as changing the number of initial adopters
The large difference between maximum and minimum is observed. When there are two initial adopters, the maximum of the final adopters expands to 62, and after this point, the maximum seldom changes and also the increasing rate of the average becomes very small after expanding sharply to about 45 final adopters, but minimum is around 1. A phenomenon begins from 6 adopters is accepted by 45 on average or two initial adopters can expand up to 62, it is possible to recognize the fashion emergence here. This proposes whether a phenomenon grows up to be fashion or not depends on initial adopters, pioneers and distribution of them.
4INTEGRATION MODEL
The previous models deal with global and individuals’ interaction separately. A next model integrates both models. E. M. Rogers points out that impersonal communication like mass media is important to recognize and personal communication is for evaluation[10]. Kawamoto verifies that impersonal communication is of grate use as information source but it does not influence to adopt and personal communication meanwhile affects people to adopt[2].
Global information informs agent of same information from the whole system is considered as impersonal communication. Local information is equivalent to personal communication like oral communication with friends or family, colleagues. In addition to the previously discussed local interaction model that the agents are influenced directly from their neighbors, the global information about adoption is introduced, so that each agent behaves according to two sources of information in this integrated model. ‘Information’ here stands for “how many agents adopts a phenomenon”.
The influence from global information becomes stronger as the number of the adopters increases, but the increasing rate per adopter is small. For example, as a song prevails, it is requested to more often radios, which makes listeners perceive it and brings to much more funs. When N is denoted as the number of the adopters, the influence of global information, GI, is as following:
GI = kNi(5)
(k, i is constant, i < 1, N is the number of adopters)
GI is renewed every step. Each agent has a threshold for the global information, if GI is higher than its threshold, the agent is influenced by the global information and its adopting rule is changed. When the threshold is p, the algorithm is:
For{
If ( p<GI)
Then rule 1
Else rule 2
Renew GI
}
In the case the agent is influenced, the new adopting rule is as following:
Pioneer:
at+1(i, j) = {1 | if LIt (i, j)<2, 0 | if LIt (i, j)2}(6)
when LI=2, pioneers keep current attitude
Follower:
at+1(i, j) = {1 | if LIt (i, j) ≧2, 0 | if LIt (i, j) <2 }(7)
Influence / 0 / 1 / 2 / 3 / 4Pioneer / ○ / ○ / △ / ☓ / ☓
Follower / ☓ / ☓ / ○ / ○ / ○
○:adopt, ☓: not adopt, △: keep current attitude
Table. 2 Adopting rule of influenced agent
Therefore this model has 4 adopting rules. Graph.3a shows the ratio of final adopters to initial adopterswhen k is 2.5 and i is 0.5 as changing the number of the pioneers and initial adopters.The expanding rate is much more than the case with local interaction only; initial adopters expand up to fifty-seven times. Local interaction model has the range that always decreases final adopters in spite of the number of pioneers, whereas integrated model doesn’t have such range but between 14 and 29 pioneers, where has two ranges of expanding rate proceeds 1.0. In this rage, initial adopters expand when there are a few initial adopters, and as initial adopters increase, final adopters reduce the number than initial adopters, and then, initial adopters expand again as initial adopters increase more.
Graph.3aThe ratio of final adopters to initial adopters(k=2.5, i=0.5)